On the size of the maximum of incomplete Kloosterman sums

@article{Bonolis2018OnTS,
  title={On the size of the maximum of incomplete Kloosterman sums},
  author={Dante Bonolis},
  journal={Mathematical Proceedings of the Cambridge Philosophical Society},
  year={2018}
}
  • Dante Bonolis
  • Published 26 November 2018
  • Mathematics
  • Mathematical Proceedings of the Cambridge Philosophical Society
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2 Citations

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ON THE DISTRIBUTION OF THE MAXIMUM OF CUBIC EXPONENTIAL SUMS

  • Youness Lamzouri
  • Mathematics
    Journal of the Institute of Mathematics of Jussieu
  • 2018
In this paper, we investigate the distribution of the maximum of partial sums of certain cubic exponential sums, commonly known as ‘Birch sums’. Our main theorem gives upper and lower bounds (of

Kloosterman paths and the shape of exponential sums

We consider the distribution of the polygonal paths joining partial sums of classical Kloosterman sums $\text{Kl}_{p}(a)$ , as $a$ varies over $\mathbf{F}_{p}^{\times }$ and as $p$ tends to infinity.

Mean Values of Character Sums

For a non-principal Dirichlet character χ modulo q, Let the Pólya-Vingradov inequality asserts that M(x) < q 1/2 log q see [7]. in the opposite direction it is a trivial consequence of lemma 1 below

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In 1918 Polya and Vinogradov gave an upper bound for the maximal size of character sums, which still remains the best known general estimate. One of the main results of this paper provides a

Lower bounds on odd order character sums

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On the conductor of cohomological transforms

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Gaussian distribution of short sums of trace functions over finite fields

Abstract We show that under certain general conditions, short sums of ℓ-adic trace functions over finite fields follow a normal distribution asymptotically when the origin varies, generalising

The distribution of the maximum of character sums

We obtain explicit bounds on the moments of character sums, refining estimates of Montgomery and Vaughan. As an application we obtain results on the distribution of the maximal magnitude of character

Exponential sums and di?erential equations

This book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differential